{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上次写了Markdown，这次用到了LaTex，也出一期（吐槽，工作量比Markdown高太多...）\n",
    "\n",
    "Markdown基础：<a href=\"https://www.cnblogs.com/dotnetcrazy/p/9180295.html\" target=\"_blank\">https://www.cnblogs.com/dotnetcrazy/p/9180295.html</a>\n",
    "\n",
    "博客园LaTex开启：<a href=\"https://www.cnblogs.com/dotnetcrazy/p/9283971.html\" target=\"_blank\">https://www.cnblogs.com/dotnetcrazy/p/9283971.html</a>\n",
    "\n",
    "\n",
    "在线预览：<a href=\"http://github.lesschina.com/python/ai/math/LaTex%20in%20Markdown.html\" target=\"_blank\">http://github.lesschina.com/python/ai/math/LaTex in Markdown.html</a>\n",
    "\n",
    "\n",
    "# 1.样式系列\n",
    "\n",
    "### 1.1.换行`\\\\`、空格`\\:`\n",
    "\n",
    "`$换行\\\\萌萌哒\\:小明$`\n",
    "\n",
    "$换行\\\\萌萌哒\\:小明$\n",
    "\n",
    "---\n",
    "\n",
    "### 1.2.居中`$$**$$`\n",
    "\n",
    "`$$萌萌哒$$`\n",
    "\n",
    "$$萌萌哒$$\n",
    "\n",
    "---\n",
    "\n",
    "### 1.3.加粗（mathbf）、斜体（mathit）\n",
    "\n",
    "```\n",
    "$\\mathbf{萌萌哒}$\n",
    "\n",
    "$\\mathit{小明}$\n",
    "```\n",
    "\n",
    "$\\mathbf{萌萌哒}$\n",
    "\n",
    "$\\mathit{小明}$\n",
    "\n",
    "---\n",
    "\n",
    "### 1.4.大小\n",
    "\n",
    "```\n",
    "$\\tiny 萌萌哒$\n",
    "\n",
    "$\\scriptsize 萌萌哒$\n",
    "\n",
    "$\\small 萌萌哒$\n",
    "\n",
    "$\\normalsize 萌萌哒(正常)$\n",
    "\n",
    "$\\large 萌萌哒$\n",
    "\n",
    "$\\Large 萌萌哒$\n",
    "\n",
    "$\\huge 萌萌哒$\n",
    "\n",
    "$\\Huge 萌萌哒$\n",
    "```\n",
    "\n",
    "$\\tiny 萌萌哒$\n",
    "\n",
    "$\\scriptsize 萌萌哒$\n",
    "\n",
    "$\\small 萌萌哒$\n",
    "\n",
    "$\\normalsize 萌萌哒(正常)$\n",
    "\n",
    "$\\large 萌萌哒$\n",
    "\n",
    "$\\Large 萌萌哒$\n",
    "\n",
    "$\\huge 萌萌哒$\n",
    "\n",
    "$\\Huge 萌萌哒$\n",
    "\n",
    "如果是单行写，记得加换行符号：\n",
    "```\n",
    "$\\tiny 萌萌哒\\\\$\n",
    "$\\scriptsize 萌萌哒\\\\$\n",
    "$\\small 萌萌哒\\\\$\n",
    "$\\normalsize 萌萌哒(正常)\\\\$\n",
    "$\\large 萌萌哒\\\\$\n",
    "$\\Large 萌萌哒\\\\$\n",
    "$\\huge 萌萌哒\\\\$\n",
    "$\\Huge 萌萌哒\\\\$\n",
    "```\n",
    "\n",
    "### ~~1.5.颜色（有些编辑器不支持）~~\n",
    "\n",
    "```\n",
    "${\\color[RGB]{255,0,0} Red}\\\\$\n",
    "${\\color[RGB]{30,144,255} Dodg Blue}\\\\$\n",
    "${\\color[RGB]{0,255,255} Aqua}\\\\$\n",
    "${\\color[RGB]{255,165,0} Orange}\\\\$\n",
    "${\\color[RGB]{255,69,0} Orange red}\\\\$\n",
    "${\\color[RGB]{0,128,0} Green}\\\\$\n",
    "${\\color[RGB]{128,128,128} Gray}\\\\$\n",
    "${\\color[RGB]{255,0,255} Magenta}\\\\$\n",
    "${\\color[RGB]{128,0,128} Purple}\\\\$\n",
    "${\\color[RGB]{184,134,11} Dark Gold}$\n",
    "```\n",
    "\n",
    "${\\color[RGB]{255,69,0} Orange red}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.常用数学\n",
    "\n",
    "### 2.1.常用表达式\n",
    "\n",
    "| 常用数学                        | LaTex公式                         |\n",
    "| ------------------------------- | --------------------------------- |\n",
    "| $\\sqrt{ab}$                     | `$\\sqrt{ab}$`                     |\n",
    "| $\\sqrt[n]{ab}$                  | `$\\sqrt[n]{ab}$`                  |\n",
    "| $\\log_{a}{b}$                   | `$\\log_{a}{b}$`                   |\n",
    "| $\\lg{ab}$                       | `$\\lg{ab}$`                       |\n",
    "| $a^{b}$                         | `$a^{b}$`                         |\n",
    "| $a_{b}$                         | `$a_{b}$`                         |\n",
    "| $x_a^b$                         | `$x_a^b$`                         |\n",
    "| $\\int$                          | `$\\int$`                          |\n",
    "| $\\int_{a}^{b}$                  | `$\\int_{a}^{b}$`                  |\n",
    "| $\\oint$                         | `$\\oint$`                         |\n",
    "| $\\oint_a^b$                     | `$\\oint_a^b$`                     |\n",
    "| $\\sum$                          | `$\\sum$`                          |\n",
    "| $\\sum_a^b$                      | `$\\sum_a^b$`                      |\n",
    "| $\\coprod$                       | `$\\coprod$`                       |\n",
    "| $\\coprod_a^b$                   | `$\\coprod_a^b$`                   |\n",
    "| $\\prod$                         | `$\\prod$`                         |\n",
    "| $\\prod_a^b$                     | `$\\prod_a^b$`                     |\n",
    "| $\\bigcap$                       | `$\\bigcap$`                       |\n",
    "| $\\bigcap_a^b$                   | `$\\bigcap_a^b$`                   |\n",
    "| $\\bigcup$                       | `$\\bigcup$`                       |\n",
    "| $\\bigcup_a^b$                   | `$\\bigcup_a^b$`                   |\n",
    "| $\\bigsqcup$                     | `$\\bigsqcup$`                     |\n",
    "| $\\bigsqcup_a^b$                 | `$\\bigsqcup_a^b$`                 |\n",
    "| $\\bigvee$                       | `$\\bigvee$`                       |\n",
    "| $\\bigvee_a^b$                   | `$\\bigvee_a^b$`                   |\n",
    "| $\\bigwedge$                     | `$\\bigwedge$`                     |\n",
    "| $\\bigwedge_a^b$                 | `$\\bigwedge_a^b$`                 |\n",
    "| $\\widetilde{ab}$                | `$\\widetilde{ab}$`                |\n",
    "| $\\widehat{ab}$                  | `$\\widehat{ab}$`                  |\n",
    "| $\\overleftarrow{ab}$            | `$\\overleftarrow{ab}$`            |\n",
    "| $\\overrightarrow{ab}$           | `$\\overrightarrow{ab}$`           |\n",
    "| $\\overbrace{ab}$                | `$\\overbrace{ab}$`                |\n",
    "| $\\underbrace{ab}$               | `$\\underbrace{ab}$`               |\n",
    "| $\\underline{ab}$                | `$\\underline{ab}$`                |\n",
    "| $\\overline{ab}$                 | `$\\overline{ab}$`                 |\n",
    "| $\\frac{ab}{cd}$                 | `$\\frac{ab}{cd}$`                 |\n",
    "| $\\frac{\\partial a}{\\partial b}$ | `$\\frac{\\partial a}{\\partial b}$` |\n",
    "| $\\frac{\\text{d}x}{\\text{d}y}$   | `$\\frac{\\text{d}x}{\\text{d}y}$`   |\n",
    "| $\\lim_{a \\rightarrow b}$        | `$\\lim_{a \\rightarrow b}$`        |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.附录：数学公式大全\n",
    "\n",
    "| 数学公式                                                               | LaTex公式                                                                |\n",
    "| ---------------------------------------------------------------------- | ------------------------------------------------------------------------ |\n",
    "| $\\displaystyle\\sum\\limits_{i=0}^n i^3$                                 | `$\\displaystyle\\sum\\limits_{i=0}^n i^3$`                                 |\n",
    "| $\\left(\\begin{array}{c}a\\\\ b\\end{array}\\right)$                        | `$\\left(\\begin{array}{c}a\\\\ b\\end{array}\\right)$`                        |\n",
    "| $\\left(\\frac{a^2}{b^3}\\right)$                                         | `$\\left(\\frac{a^2}{b^3}\\right)$`                                         |\n",
    "| $\\left.\\frac{a^3}{3}\\right\\lvert_0^1$                                      | `$\\left.\\frac{a^3}{3}\\right\\lvert_0^1$`                                       |\n",
    "| $\\begin{bmatrix}a & b \\\\c & d \\end{bmatrix}$                           | `$\\begin{bmatrix}a & b \\\\c & d \\end{bmatrix}$`                           |\n",
    "| $\\begin{cases}a & x = 0\\\\b & x > 0\\end{cases}$                         | `$\\begin{cases}a & x = 0\\\\b & x > 0\\end{cases}$`                         |\n",
    "| $\\sqrt{\\frac{n}{n-1} S}$                                               | `$\\sqrt{\\frac{n}{n-1} S}$`                                               |\n",
    "| $\\begin{pmatrix} \\alpha& \\beta^{*}\\\\ \\gamma^{*}& \\delta \\end{pmatrix}$ | `$\\begin{pmatrix} \\alpha& \\beta^{*}\\\\ \\gamma^{*}& \\delta \\end{pmatrix}$` |\n",
    "| $A\\:\\xleftarrow{n+\\mu-1}\\:B$                                           | `$A\\:\\xleftarrow{n+\\mu-1}\\:B$`                                           |\n",
    "| $B\\:\\xrightarrow[T]{n\\pm i-1}\\:C$                                      | `$B\\:\\xrightarrow[T]{n\\pm i-1}\\:C$`                                      |\n",
    "| $\\frac{1}{k}\\log_2 c(f)\\;$                                             | `$\\frac{1}{k}\\log_2 c(f)\\;$`                                             |\n",
    "| $\\iint\\limits_A f(x,y)\\;$                                              | `$\\iint\\limits_A f(x,y)\\;$`                                              |\n",
    "| $x^n + y^n = z^n$                                                      | `$x^n + y^n = z^n$`                                                      |\n",
    "| $E=mc^2$                                                               | `$E=mc^2$`                                                               |\n",
    "| $e^{\\pi i} - 1 = 0$                                                    | `$e^{\\pi i} - 1 = 0$`                                                    |\n",
    "| $p(x) = 3x^6$                                                          | `$p(x) = 3x^6$`                                                          |\n",
    "| $3x + y =  12$                                                         | `$3x + y =  12$`                                                         |\n",
    "| $\\int_0^\\infty \\mathrm{e}^{-x}\\,\\mathrm{d}x$                           | `$\\int_0^\\infty \\mathrm{e}^{-x}\\,\\mathrm{d}x$`                           |\n",
    "| $\\sqrt[n]{1+x+x^2+\\ldots}$                                             | `$\\sqrt[n]{1+x+x^2+\\ldots}$`                                             |\n",
    "| $\\binom{x}{y} = \\frac{x!}{y!(x-y)!}$                                   | `$\\binom{x}{y} = \\frac{x!}{y!(x-y)!}$`                                   |\n",
    "| $\\frac{\\frac{1}{x}+\\frac{1}{y}}{y-z}$                                  | `$\\frac{\\frac{1}{x}+\\frac{1}{y}}{y-z}$`                                  |\n",
    "| $f(x)=\\frac{P(x)}{Q(x)}$                                               | `$f(x)=\\frac{P(x)}{Q(x)}$`                                               |\n",
    "| $\\frac{1+\\frac{a}{b}}{1+\\frac{1}{1+\\frac{1}{a}}}$                      | `$\\frac{1+\\frac{a}{b}}{1+\\frac{1}{1+\\frac{1}{a}}}$`                      |\n",
    "| $\\sum_{\\substack{0\\le i\\le m\\\\ 0\\lt j\\lt n}} P(i,j)$                   | `$\\sum_{\\substack{0\\le i\\le m\\\\ 0\\lt j\\lt n}} P(i,j)$`                   |\n",
    "| $\\lim_{x \\to \\infty} \\exp(-x) = 0$                                     | `$\\lim_{x \\to \\infty} \\exp(-x) = 0$`                                     |\n",
    "| $\\cos (2\\theta) = \\cos^2 \\theta - \\sin^2 \\theta$                       | `$\\cos (2\\theta) = \\cos^2 \\theta - \\sin^2 \\theta$`                       |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.数学符号\n",
    "\n",
    "### 3.1.集合系列\n",
    "\n",
    "| 运算符          | 公式              | 运算符           | 公式               | 运算符           | 公式               |\n",
    "| --------------- | ----------------- | ---------------- | ------------------ | ---------------- | ------------------ |\n",
    "| $\\emptyset$     | `$\\emptyset$`     | $\\in$            | `$\\in$`            | $\\notin$         | `$\\notin$`         |\n",
    "| $\\subset$       | `$\\subset$`       | $\\supset$        | `$\\supset$`        | $\\subseteq$      | `$\\subseteq$`      |\n",
    "| $\\nsubseteq$    | `$\\nsubseteq$`    | $\\nsupseteq$     | `$\\nsupseteq$`     | $\\nsubseteqq$    | `$\\nsubseteqq$`    |\n",
    "| $\\nsupseteqq$   | `$\\nsupseteqq$`   | $\\subsetneq$     | `$\\subsetneq$`     | $\\supsetneq$     | `$\\supsetneq$`     |\n",
    "| $\\subsetneqq$   | `$\\subsetneqq$`   | $\\supsetneqq$    | `$\\supsetneqq$`    | $\\varsubsetneq$  | `$\\varsubsetneq$`  |\n",
    "| $\\varsupsetneq$ | `$\\varsupsetneq$` | $\\varsubsetneqq$ | `$\\varsubsetneqq$` | $\\varsupsetneqq$ | `$\\varsupsetneqq$` |\n",
    "| $\\bigcap$       | `$\\bigcap$`       | $\\bigcup$        | `$\\bigcup$`        | $\\bigvee$        | `$\\bigvee$`        |\n",
    "| $\\bigwedge$     | `$\\bigwedge$`     | $\\biguplus$      | `$\\biguplus$`      | $\\bigsqcup$      | `$\\bigsqcup$`      |\n",
    "| $\\Subset$       | `$\\Subset$`       | $\\Supset$        | `$\\Supset$`        | $\\subseteqq$     | `$\\subseteqq$`     |\n",
    "| $\\supseteqq$    | `$\\supseteqq$`    | $\\sqsubset$      | `$\\sqsubset$`      | $\\sqsupset$      | `$\\sqsupset$`      |\n",
    "\n",
    "---\n",
    "\n",
    "### 3.2.常用符号\n",
    "\n",
    "| 基本符号         | 公式               | 基本符号          | 公式                | 基本符号        | 公式              |\n",
    "| ---------------- | ------------------ | ----------------- | ------------------- | --------------- | ----------------- |\n",
    "| $\\cdot$          | `$\\cdot$`          | $\\vdots$          | `$\\vdots$`          | $\\grave{x}$     | `$\\grave{x}$`     |\n",
    "| $.$              | `$.$`              | $\\ddots$          | `$\\ddots$`          | $\\breve{x}$     | `$\\breve{x}$`     |\n",
    "| $*$              | `$*$`              | $,$               | `$,$`               | $\\dot{x}$       | `$\\dot{x}$`       |\n",
    "| $+$              | `$+$`              | $!$               | `$!$`               | $\\widehat{xxx}$ | `$\\widehat{xxx}$` |\n",
    "| $-$              | `$-$`              | $;$               | `$;$`               | $\\ddot{x}$      | `$\\ddot{x}$`      |\n",
    "| $\\times$         | `$\\times$`         | $?$               | `$?$`               | $\\check{x}$     | `$\\check{x}$`     |\n",
    "| $\\div$           | `$\\div$`           | $\\colon$          | `$\\colon$`          | $\\ddot{x}$      | `$\\ddot{x}$`      |\n",
    "| $=$              | `$=$`              | $\\acute{x}$       | `$\\acute{x}$`       | $\\tilde{x}$     | `$\\tilde{x}$`     |\n",
    "| $\\neq$           | `$\\neq$`           | $\\bar{x}$         | `$\\bar{x}$`         | $\\hat{x}$       | `$\\hat{x}$`       |\n",
    "| $\\dotsm$         | `$\\dotsm$`         | $\\vec{x}$         | `$\\vec{x}$`         | $\\dddot{x}$     | `$\\dddot{x}$`     |\n",
    "| $\\dotso$         | `$\\dotso$`         | $\\widetilde{xxx}$ | `$\\widetilde{xxx}$` | $\\backslash$    | `$\\backslash$`    |\n",
    "| $/$              | `$/$`              | $\\bracevert$      | `$\\bracevert$`      | $]$             | `$]$`             |\n",
    "| $\\smallsetminus$ | `$\\smallsetminus$` | $\\lVert$          | `$\\lVert$`          | $\\lbrace$       | `$\\lbrace$`       |\n",
    "| $\\arrowvert$     | `$\\arrowvert$`     | $\\rVert$          | `$\\rVert$`          | $\\rbrace$       | `$\\rbrace$`       |\n",
    "| $\\lvert$         | $\\lvert$           | $\\lgroup$         | `$\\lgroup$`         | $\\langle$       | `$\\langle$`       |\n",
    "| $\\lvert$         | `$\\lvert$`         | $\\rgroup$         | `$\\rgroup$`         | $\\rangle$       | `$\\rangle$`       |\n",
    "| $\\rvert$         | `$\\rvert$`         | $[$               | `$[$`               | $\\lmoustache$   | `$\\lmoustache$`   |\n",
    "| $\\rmoustache$    | `$\\rmoustache$`    | $\\lceil$          | `$\\lceil$`          | $\\rceil$        | `$\\rceil$`        |\n",
    "| $\\lfloor$        | `$\\lfloor$`        | $\\rfloor$         | `$\\rfloor$`         |\n",
    "\n",
    "---\n",
    "\n",
    "### 3.3.希腊字母表\n",
    "\n",
    "| 字母          | 公式            | 字母        | 公式          | 字母        | 公式          |\n",
    "| ------------- | --------------- | ----------- | ------------- | ----------- | ------------- |\n",
    "| $\\alpha$      | `$\\alpha$`      | $\\beta$     | `$\\beta$`     | $\\chi$      | `$\\chi$`      |\n",
    "| $\\delta$      | `$\\delta$`      | $\\Delta$    | `$\\Delta$`    | $\\epsilon$  | `$\\epsilon$`  |\n",
    "| $\\eta$        | `$\\eta$`        | $\\Gamma$    | `$\\Gamma$`    | $\\iota$     | `$\\iota$`     |\n",
    "| $\\kappa$      | `$\\kappa$`      | $\\lambda$   | `$\\lambda$`   | $\\Lambda$   | `$\\Lambda$`   |\n",
    "| $\\mu$         | `$\\mu$`         | $\\nabla$    | `$\\nabla$`    | $\\nu$       | `$\\nu$`       |\n",
    "| $\\omega$      | `$\\omega$`      | $\\Omega$    | `$\\Omega$`    | $\\phi$      | `$\\phi$`      |\n",
    "| $\\Phi$        | `$\\Phi$`        | $\\pi$       | `$\\pi$`       | $\\Pi$       | `$\\Pi$`       |\n",
    "| $\\psi$        | `$\\psi$`        | $\\Psi$      | `$\\Psi$`      | $\\rho$      | `$\\rho$`      |\n",
    "| $\\sigma$      | `$\\sigma$`      | $\\Sigma$    | `$\\Sigma$`    | $\\tau$      | `$\\tau$`      |\n",
    "| $\\theta$      | `$\\theta$`      | $\\Theta$    | `$\\Theta$`    | $\\upsilon$  | `$\\upsilon$`  |\n",
    "| $\\varepsilon$ | `$\\varepsilon$` | $\\varsigma$ | `$\\varsigma$` | $\\vartheta$ | `$\\vartheta$` |\n",
    "| $\\xi$         | `$\\xi$`         | $\\zeta$     | `$\\zeta$`     |\n",
    "\n",
    "---\n",
    "\n",
    "### 3.4.函数公式表\n",
    "\n",
    "| 函数              | 公式                | 函数         | 公式           | 函数          | 公式            |\n",
    "| ----------------- | ------------------- | ------------ | -------------- | ------------- | --------------- |\n",
    "| $\\sin$            | `$\\sin$`            | $\\sin^{-1}$  | `$\\sin^{-1}$`  | $\\inf$        | `$\\inf$`        |\n",
    "| $\\cos$            | `$\\cos$`            | $\\cos^{-1}$  | `$\\cos^{-1}$`  | $\\arg$        | `$\\arg$`        |\n",
    "| $\\tan$            | `$\\tan$`            | $\\tan^{-1}$  | `$\\tan^{-1}$`  | $\\det$        | `$\\det$`        |\n",
    "| $\\sinh$           | `$\\sinh$`           | $\\sinh^{-1}$ | `$\\sinh^{-1}$` | $\\dim$        | `$\\dim$`        |\n",
    "| $\\cosh$           | `$\\cosh$`           | $\\cosh^{-1}$ | `$\\cosh^{-1}$` | $\\gcd$        | `$\\gcd$`        |\n",
    "| $\\tanh$           | `$\\tanh$`           | $\\tanh^{-1}$ | `$\\tanh^{-1}$` | $\\hom$        | `$\\hom$`        |\n",
    "| $\\csc$            | `$\\csc$`            | $\\exp$       | `$\\exp$`       | $\\ker$        | `$\\ker$`        |\n",
    "| $\\sec$            | `$\\sec$`            | $\\lg$        | `$\\lg$`        | $\\Pr$         | `$\\Pr$`         |\n",
    "| $\\cot$            | `$\\cot$`            | $\\ln$        | `$\\ln$`        | $\\sup$        | `$\\sup$`        |\n",
    "| $\\coth$           | `$\\coth$`           | $\\log$       | `$\\log$`       | $\\deg$        | `$\\deg$`        |\n",
    "| $\\hom$            | `$\\hom$`            | $\\log_{e}$   | `$\\log_{e}$`   | $\\injlim$     | `$\\injlim$`     |\n",
    "| $\\arcsin$         | `$\\arcsin$`         | $\\log_{10}$  | `$\\log_{10}$`  | $\\varinjlim$  | `$\\varinjlim$`  |\n",
    "| $\\arccos$         | `$\\arccos$`         | $\\lim$       | `$\\lim$`       | $\\varprojlim$ | `$\\varprojlim$` |\n",
    "| $\\det$            | `$\\det$`            | $\\liminf$    | `$\\liminf$`    | $\\varliminf$  | `$\\varliminf$`  |\n",
    "| $\\arctan$         | `$\\arctan$`         | $\\limsup$    | `$\\limsup$`    | $\\projlim$    | `$\\projlim$`    |\n",
    "| $\\textrm{arccsc}$ | `$\\textrm{arccsc}$` | $\\max$       | `$\\max$`       | $\\varlimsup$  | `$\\varlimsup$`  |\n",
    "| $\\textrm{arcsec}$ | `$\\textrm{arcsec}$` | $\\min$       | `$\\min$`       |\n",
    "| $\\textrm{arccot}$ | `$\\textrm{arccot}$` | $\\infty$     | `$\\infty$`     |\n",
    "\n",
    "---\n",
    "\n",
    "### 3.5.特殊符号-箭头系列\n",
    "\n",
    "---\n",
    "\n",
    "| 箭头                | 公式                  | 箭头                  | 公式                    | 箭头                   | 公式                     |\n",
    "| ------------------- | --------------------- | --------------------- | ----------------------- | ---------------------- | ------------------------ |\n",
    "| $\\uparrow$          | `$\\uparrow$`          | $\\longleftarrow$      | `$\\longleftarrow$`      | $\\downdownarrows$      | `$\\downdownarrows$`      |\n",
    "| $\\downarrow$        | `$\\downarrow$`        | $\\longrightarrow$     | `$\\longrightarrow$`     | $\\upuparrows$          | `$\\upuparrows$`          |\n",
    "| $\\updownarrow$      | `$\\updownarrow$`      | $\\rightarrow$         | `$\\rightarrow$`         | $\\rightharpoondown$    | `$\\rightharpoondown$`    |\n",
    "| $\\Uparrow$          | `$\\Uparrow$`          | $\\leftarrow$          | `$\\leftarrow$`          | $\\downharpoonleft$     | `$\\downharpoonleft$`     |\n",
    "| $\\Downarrow$        | `$\\Downarrow$`        | $\\mapsto$             | `$\\mapsto$`             | $\\rightharpoonup$      | `$\\rightharpoonup$`      |\n",
    "| $\\Leftarrow$        | `$\\Leftarrow$`        | $\\nrightarrow$        | `$\\nrightarrow$`        | $\\downharpoonright$    | `$\\downharpoonright$`    |\n",
    "| $\\Rightarrow$       | `$\\Rightarrow$`       | $\\nleftarrow$         | `$\\nleftarrow$`         | $\\upharpoonleft$       | `$\\upharpoonleft$`       |\n",
    "| $\\Leftrightarrow$   | `$\\Leftrightarrow$`   | $\\rightrightarrows$   | `$\\rightrightarrows$`   | $\\upharpoonright$      | `$\\upharpoonright$`      |\n",
    "| $\\nLeftrightarrow$  | `$\\nLeftrightarrow$`  | $\\leftleftarrows$     | `$\\leftleftarrows$`     | $\\leftharpoondown$     | `$\\leftharpoondown$`     |\n",
    "| $\\nLeftarrow$       | `$\\nLeftarrow$`       | $\\rightleftarrows$    | `$\\rightleftarrows$`    | $\\leftharpoonup$       | `$\\leftharpoonup$`       |\n",
    "| $\\nRightarrow$      | `$\\nRightarrow$`      | $\\leftrightarrows$    | `$\\leftrightarrows$`    | $\\hookleftarrow$       | `$\\hookleftarrow$`       |\n",
    "| $\\Updownarrow$      | `$\\Updownarrow$`      | $\\curvearrowleft$     | `$\\curvearrowleft$`     | $\\hookrightarrow$      | `$\\hookrightarrow$`      |\n",
    "| $\\circlearrowleft$  | `$\\circlearrowleft$`  | $\\curvearrowright$    | `$\\curvearrowright$`    | $\\rightleftharpoons$   | `$\\rightleftharpoons$`   |\n",
    "| $\\circlearrowright$ | `$\\circlearrowright$` | $\\Longleftarrow$      | `$\\Longleftarrow$`      | $\\leftrightharpoons$   | `$\\leftrightharpoons$`   |\n",
    "| $\\Lleftarrow$       | `$\\Lleftarrow$`       | $\\Longrightarrow$     | `$\\Longrightarrow$`     | $\\looparrowleft$       | `$\\looparrowleft$`       |\n",
    "| $\\Rrightarrow$      | `$\\Rrightarrow$`      | $\\longleftrightarrow$ | `$\\longleftrightarrow$` | $\\looparrowright$      | `$\\looparrowright$`      |\n",
    "| $\\nwarrow$          | `$\\nwarrow$`          | $\\Longleftrightarrow$ | `$\\Longleftrightarrow$` | $\\rightsquigarrow$     | `$\\rightsquigarrow$`     |\n",
    "| $\\swarrow$          | `$\\swarrow$`          | $\\longmapsto$         | `$\\longmapsto$`         | $\\Lsh$                 | `$\\Lsh$`                 |\n",
    "| $\\searrow$          | `$\\searrow$`          | $\\rightarrowtail$     | `$\\rightarrowtail$`     | $\\Rsh$                 | `$\\Rsh$`                 |\n",
    "| $\\nearrow$          | `$\\nearrow$`          | $\\leftarrowtail$      | `$\\leftarrowtail$`      | $\\multimap$            | `$\\multimap$`            |\n",
    "| $\\twoheadleftarrow$ | `$\\twoheadleftarrow$` | $\\twoheadrightarrow$  | `$\\twoheadrightarrow$`    | $\\leftrightsquigarrow$ | `$\\leftrightsquigarrow$` |\n",
    "| $\\leftrightarrow$   | `$\\leftrightarrow$`   | $\\nleftrightarrow$    | `$\\nleftrightarrow$`    |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.逆天常用\n",
    "\n",
    "逆天用到就添加进去（不定期更新）根据上面有的，这些其实都可以自己写出来的\n",
    "\n",
    "### 4.1.二次方程求解\n",
    "\n",
    "```\n",
    "$\\mathbf{a*x^2+b*x+c}$\n",
    "\n",
    "$$x={\\frac{-b \\pm \\sqrt{b^2-4ac}}{2a}}$$ or $$x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}$$\n",
    "```\n",
    "\n",
    "$\\mathbf{a*x^2+b*x+c}$\n",
    "\n",
    "$$x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}$$\n",
    "\n",
    "---\n",
    "\n",
    "### 4.2.矩阵系列\n",
    "\n",
    "```\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "1&0&0 \\\\\n",
    "0&1&0 \\\\\n",
    "0&0&1\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "```\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "1&0&0 \\\\\n",
    "0&1&0 \\\\\n",
    "0&0&1\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "---\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
